# How do you write an equation of the line with f(-2)=1 and f(-1)=3?

Jul 15, 2015

$y = 2 x + 5$ in slope-intercept form and $2 x - y + 5 = 0$ in standard form.

#### Explanation:

The slope of the line is

$\setminus \frac{\setminus m b \otimes \left\{r i s e\right\}}{\setminus m b \otimes \left\{r u n\right\}} = \setminus \frac{\setminus \Delta y}{\setminus \Delta x} = \setminus \frac{f \left(- 1\right) - f \left(- 2\right)}{- 1 - \left(- 2\right)} = \setminus \frac{3 - 1}{- 1 + 2} = \frac{2}{1} = 2$

Therefore, the equation of the line can be written (in point-slope form) as

$y = 2 \left(x - \left(- 2\right)\right) + 1 = 2 \left(x + 2\right) + 1$.

Using the distributive property and simplifying gives the slope-intercept form

$y = 2 x + 5$.

Rearranging gives the standard form

$2 x - y + 5 = 0$.